# Diagnosing the regression to see what's wrong and what's right.

We can use the fairly innovative GLVMA statistic from Peña and Slate (2006) to assess the model with a linear and non-linear response. Rather unsurprisingly they both come out with some problems, most notbly that there are linearities involved. For the model using co2:

gvlma(x = my.model)

Value p-value Decision

Global Stat 33.3035 1.035e-06 Assumptions NOT satisfied!

Skewness 2.7901 9.485e-02 Assumptions acceptable.

Kurtosis 4.6877 3.038e-02 Assumptions NOT satisfied!

Link Function 25.3560 4.767e-07 Assumptions NOT satisfied!

Heteroscedasticity 0.4698 4.931e-01 Assumptions acceptable.

And using log co2 difference:

Global Stat 3.065e+02 0.000e+00 Assumptions NOT satisfied!

Skewness 8.434e-03 9.268e-01 Assumptions acceptable.

Kurtosis 1.391e+02 0.000e+00 Assumptions NOT satisfied!

Link Function 9.804e+01 0.000e+00 Assumptions NOT satisfied!

Heteroscedasticity 6.931e+01 1.110e-16 Assumptions NOT satisfied!

Interpreting this is a bit of a black art, but it seems to me that the linear model is less invalid than the non-linear one. I think at least in the linear model, the skewness and kurtosis are significant because of dependence on the link function (testing for overall linearity of the model). Whereas with larger, and more significant significant terms for the non-linear model, there are other problems.

This doesn't really matter any way, as we can look at the diagnostic graphs produced by the gvlma package which are straightforward. It's certainly very difficult to envisage any other reason other than increasing greenhouse gas concentration for the rising temperatures observed.

The graphs show clearly that volcanic doesn't do a very good job of predicting anomaly, solar is rather better, and co2 is lock step. Anomaly versus time sequence for directional stat 4 does a very good job of nixing the asertion that the earth has started cooling. What we're really seeing there is evidence for an interesting trend for warming followed by an abrupt temperature drop (with a minimum higher than the minimum of the last period) followed by a further rise. There's certainly no evidence to suggest that "global warming has stopped", which is one of the most idiotic assertions of the climate skeptic brigade.

Peña, E. A., & Slate, E. H. (2006). Global Validation of Linear Model Assumptions. Journal of the American Statistical Association, 101(473), 341-354. doi: 10.1198/016214505000000637.

Next up, regression diagnostics over a thousand or so years here: Solar ...

Here's an similar graph from Lean, J., Beer, J. and Bradley, R. 1995. Reconstruction of solar irradiance since 1610: Implications for climate change. Geophysical Research Letters 22: 3195-3198:

# Truncating the data.

climate.summary.end <- subset(climate.summary, climate$Year > 1979)

> summary(my.short.model)

Call:

lm(formula = ANOMALY ~ SOLAR + co2_mean, data = climate.summary.end)

Residuals:

Min 1Q Median 3Q Max

-0.19938 -0.05220 0.03270 0.06071 0.09708

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) -2.366450 0.794575 -2.978 0.00806 **

SOLAR 0.688377 0.348307 1.976 0.06364 .

co2_mean 0.007756 0.002140 3.625 0.00194 **

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.09009 on 18 degrees of freedom

(8 observations deleted due to missingness)

Multiple R-squared: 0.4563, Adjusted R-squared: 0.3959

F-statistic: 7.553 on 2 and 18 DF, p-value: 0.004153

> gvlma(my.short.model)

Call:

lm(formula = ANOMALY ~ SOLAR + co2_mean, data = climate.summary.end)

Coefficients:

(Intercept) SOLAR co2_mean

-2.366450 0.688377 0.007756

ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS

USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:

Level of Significance = 0.05

Call:

gvlma(x = my.short.model)

Value p-value Decision

Global Stat 8.16221 0.08581 Assumptions acceptable.

Skewness 3.35623 0.06695 Assumptions acceptable.

Kurtosis 0.01176 0.91363 Assumptions acceptable.

Link Function 4.28587 0.03843 Assumptions NOT satisfied!

Heteroscedasticity 0.50834 0.47586 Assumptions acceptable.

plot.gvlma(gvlma(my.short.model))

So you see some cyclical change in variability. Is this solar or is it ENSO or is it something else?

Scaling the same model is also useful:

lm(formula = scale(ANOMALY) ~ scale(SOLAR) + scale(co2_mean), data = climate.summary.end)

Call:

lm(formula = scale(ANOMALY) ~ scale(SOLAR) + scale(co2_mean), data = climate.summary.end)

Coefficients:

(Intercept) scale(SOLAR) scale(co2_mean)

0.4280 0.3665 0.9426

which shows that co2 is 3 times more important than solar in the prediction of anomaly. With the whole model explaining 76% of the variance you can do the maths on the relative contributions.

## Comments (Show all 111)

## kenlambert said

at 10:25 pm on Aug 9, 2009

The commentary on the S&W paper was from a different source than the paper which I found directly on the web. I agree that the commentator should not have mentioned the 60% without also quoting the lower limit (whatever that was). A minor indiscretion compared to the IPCC claims which places CO2 forcing at 92% and Solar forcing at 8% relative to 1750AD in AR4 Fig 2.4. Agree??

Moving on to the important bits:

Your short 1978 - 2008? run shows some intriguing results and cyclical patterns:

1) For the 76% explained by CO2 and Solar; ratio of CO2:Solar is 2.57:1 which is 72%CO2 and 28% Solar. Plumb in the range of 25%-35% Solar for the 1980-2000 period from the S&W paper. Kieren you are amazing!!

What are the odds of Scafetta and West being in agreement with you on both paleface??

2) The T vs Co2 mean, T vs Time Stat 4, and Resdiuals vs Time Stat 4 all show a cyclical pattern. Is the Time Stat 4 scale in years? If so it seems to match a roughly 11 year cycle - a Solar cycle.

I seem to remember Solar and CO2 showing a strong correlation from the Stage 1 Analysis.

I thought ENSO was a SH phenomenon - are you still using the NH Temp Anomaly set?

Otherwise cyclical CO2 and Temp can only mean Temp is rising AND falling with a continually rising CO2 - could this indicate that a CO2 saturation effect is occuring? The Co2 greenhouse gas absorber is not a one way window. It can gain Temp (heat) and lose Temp (heat) while steadily rising in concentration.

If the Time Stat axis is years - the 11 year Solar cycle is the likely culprit.

## Kieren Diment said

at 10:39 pm on Aug 9, 2009

I don't actually understand the "IPCC claims which places CO2 forcing at 92% and Solar forcing at 8% relative to 1750AD in AR4 Fig 2.4" at all well, so I couldn't possibly have an opinon on who's right, you or the IPCC. I think if you start taking partial correlations, you might see something like the IPCC figures (i.e. solar forcing with the effect of co2 removed), but I'd have to remember where I put the figures.

ENSO affects weather globally. Obviously any honest analysis at the same time frame with similar data will come to the same conclusion, so it's not surprising that what I've done is in agreement with others.

"Otherwise cyclical CO2 and Temp can only mean Temp is rising AND falling with a continually rising CO2 - could this indicate that a CO2 saturation effect is occuring? The Co2 greenhouse gas absorber is not a one way window. It can gain Temp (heat) and lose Temp (heat) while steadily rising in concentration."

This comment has two problems. One is that it doesn't make much sense. Two, the long term trend is clearly rapid rise in temperature, as seen on the http://climatekaraoke.pbworks.com/Idiot page (second graph is much clearer) of greater magnitude than anything else over the past thousand years.

Finally need to acknowledge the potential positive feedback that we're seeing evidence for at the end of the time series. Failing to do so is being very selective with the results that you want to consider, and it's not good for your credibility.

## kenlambert said

at 11:05 pm on Aug 9, 2009

This is from Summary for Policy Makers IPCC AR4:

Note that the FIG 2.4. from the Main Report has been re-named SPM2 in the Summary for Policymakers)

"The understanding of anthropogenic warming and

cooling infl uences on climate has improved since

the TAR, leading to very high confi dence7 that the

global average net effect of human activities since

1750 has been one of warming, with a radiative

forcing of +1.6 [+0.6 to +2.4] W m–2 (see Figure

SPM.2). {2.3., 6.5, 2.9}"

AND

• Changes in solar irradiance since 1750 are estimated

to cause a radiative forcing of +0.12 [+0.06 to +0.30]

W m–2, which is less than half the estimate given in the

TAR. {2.7}

Ref: http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_SPM.pdf

## kenlambert said

at 11:07 pm on Aug 9, 2009

This is what PM Rudd and Minsiter Wong read before bedtime.

## kenlambert said

at 11:51 pm on Aug 10, 2009

http://climate.envsci.rutgers.edu/pdf/StottEtAl.pdf

"Nevertheless, our main conclusion, that models underestimate

the climatic response to solar forcing, is

supported by two other detection studies that used diagnostics

tailored for the 11-yr solar cycle. Hill et al.

(2001) showed that models underestimate the tropospheric

temperature response to solar forcing by a factor

of 2 to 3 and North and Wu (2001) found an underestimate

of about 2 for near-surface temperatures.

These results indicate that climatic processes, not

present in the model, have acted to alter the magnitude

of the large-scale spatial and temporal near-surface temperature

response. Our methodology is not designed to

identify missing processes that alter small-scale details

of the response. Although our study indicates that there

could be an enhanced global-scale temperature response

to solar forcing, convincing evidence for a mechanism

remains elusive. Potentially the largest amplification of

solar forcing could result from modulation of stratospheric

ozone by variations in solar ultraviolet, which

could influence the troposphere via modulation of planetary

waves (Shindell et al. 1999b) or modulation of

the Hadley circulation (Haigh 1996), although none of

the published studies indicate that ozone feedback could

enhance solar radiative forcing by more than a factor

of one-half (J. D. Haigh 2003, personal communication).

...next half....

## kenlambert said

at 11:52 pm on Aug 10, 2009

Alternatively, solar effects on climate could be mediated

by cosmic rays, the intensity of which has declined at

the earth as the interplanetary magnetic field increased

during the twentieth century. It has been speculated that

cosmic rays could modulate global temperature by

changing clouds (Marsh and Svensmark 2000; Yu 2002)

or by altering the global electric circuit (Harrison 2002).

The results presented here suggest that climate models

underestimate the sensitivity of the climate system to

changes in solar irradiance, but a conclusive demonstration

of an enhanced role for solar forcing requires

an understanding of the physical mechanisms underlying

such an effect.*

## kenlambert said

at 11:58 pm on Aug 10, 2009

The above reference spun from your Wiki 'Solar' reference.

It splits the last 100 years into 1900 -1949 and 1950-1999 - gets Solar:GHG 53%/47% in the first half century and Solar at 16-36% in the secong half, but higher in the last 30 years?? Lots of regression analysis for you to compare.

## Kieren Diment said

at 7:50 am on Aug 11, 2009

Apparently the cosmic ray theory is a furphy: http://en.wikipedia.org/wiki/Global_warming#Solar_variation

## Kieren Diment said

at 7:51 am on Aug 11, 2009

Ken,

You still haven't touched my positive feedback theory. This is just about the most important and most relevant thing in this set of analysis, so I'm a bit shocked that you're totally ignoring it.

## kenlambert said

at 10:09 pm on Aug 11, 2009

kdkd

I'm all ears Kieren. Fill us in on your feedback theory - show some references and describe a mechanism.

I note you have ignored my conclusive points about the misleading nature of IPCC AR4 'Radiative Forcings' - even you now can see that the contribution of Solar forcings has been very significant - up to 45% of the last 100 years warming, and 25-30% of the warming since approx 1980 using the IPCC's own source data.

Which puts us back into the cage fight and Crikey comments where I made the consistent point that the panic is all about the last 25-30 years of temperature data - the last 10 of which have flattened or cooled since the 1998 ENSO high peak and aftermath.

Here is what you say about doing a comprehensive forcing 1980-2008 run on AUG9:

*There's no point in doing a short time range of analysis of everything as the sample size is too small. We can already see that at a short term time range all of the short-term variability masks the long-term variability.*

You don't seem too keen on thououghly analysing the last 25-30 years - not enough data points - yet happy enough to accept the results when they appear to favour a CO2 answer.

See next post for an interesting comparison of the GISS and UAH data.

## Kieren Diment said

at 10:42 pm on Aug 11, 2009

Ken: well the fact that these solar forcings are a. not independent of CO2 (as we see from the link function statistic), and b. this dependence has reduced in the past 20-odd years since CO2 has taken over as the main driver of temperature change "up to" (weasel words?) 45% reducing to 25-30%? There's evidence for a mechanism already.

The residual analysis clearly points to the existence of a positive feedback. Albedo, and methane production from melting tundra are both possible candidates.

If 1980-2008 data broadly suports existing conclusions, then there's no controversy (this is what we see for the most part, but with a lower signal to noise ratio). If it's in sharp contradiction to other data then we have a situation where we can make new hypothesis. Unfortunately for you, the meager inconsistencies with the rest of the data point to a positive feedback mechanism, not a negative feedback mechainsm.

## kenlambert said

at 11:54 pm on Aug 11, 2009

I know it hurts to have that 45% Solar mentioned, but that is what your analysis produced paleface!! I won't use 'up to'........ just 'at'!

Check out the differences between UAH and GISS Temp Data here:

http://wattsupwiththat.com/2009/06/24/a-comphrehensive-comparison-of-giss-and-uah-global-temperature-data/

Check out Dutch alternative data sets here:

http://climexp.knmi.nl/selectfield_obs2.cgi?someone@somewhere

Show us some data for the Methane and Tundra Albedo effects and why the (Solar 11 year?) cyclical nature of these feedbacks which I assume comes from the signature of the residuals.

## Kieren Diment said

at 7:51 am on Aug 12, 2009

Ken

There's a lot of wishful thinking going on in your commentary. Firstly the wattsup with that data doesn't support your conclusions unless you squint and ignore the statistical evidence.

It's not my job to find data, it's yours. You asked for a hypothesis, I gave you wan. You want proof, you find the data.

And the tempreature anomaly data at http://climexp.knmi.nl/selectfield_obs2.cgi seems quite consistent with the IPCC data. There is a lot of data there though, that's probably worth exploring. However, it's going to be a lot of work for you to corral it together in a coherent way for further analysis.

## kenlambert said

at 12:21 am on Aug 13, 2009

I have proposed 6 Hypotheticals on JUL28 and 4 Propositions on AUG8. Are you going to find data for those?

I don't agree that the UAH Temp data is statistically consistent with the GISS data. I stick with the comments in the cage fight. The 1997-98 ENSO is a disruptive spike which has displaced a two relatively flat trends - and a linear trend line for the whole 30 year period is misleading.

Your consistent line that the CO2 + Solar underestimate Temp is still based on the IPCC-GISS Northern Hemisphere data. You ignored my points about SH being 65% of NH *trend* and probably less than linear. A global set of data should be used.

The variation in the sun's TSI is a combination of output and orbital proximity - not CO2 related.

You seem to still be unclear that Solar forcing is the variation in incoming radiation - not the portion absorbed by CO2 and other GHG (greenhouse effect variations in forcing).

The sun does not know that CO2 on Earth is increasing; so if the Solar forcing variation and CO2 forcing (log diff relationship) are cyclically related, it cannot be CO2 driven - it can only be Solar driven, can't it?? Any other explanation?

## Kieren Diment said

at 12:34 am on Aug 13, 2009

Ken,

Disagree all about the consistency of UAH / GISS all you like. But your disagreement belongs in the faculty of making data up - it's not supported by the data.

## Kieren Diment said

at 7:03 am on Aug 13, 2009

Ken

Or to be more clear about it. If you have specific objections to my interpretation of the UAH data cf the GISS data, which the statistics clearly and quantitatively show are comparable to each other, and statistically consistent, then you have to explain that objection clearly and quantitiatively. In my objective (in that the analysis is done without any reference to my preconceptions) quantitative analysis versus your qualitative analysis, my quantitative analysis wins every time.

Oh yeah. I don't have masses of time to deal with this stuff. If you want complex data analyzed, provide me with the tables.

## kenlambert said

at 11:59 pm on Aug 13, 2009

I get an hour or two at night to indulge in saving the planet with you Kieren. The rest of the time I devote to my family and employing people, designing and exporting things.

I found and lost a website with a global set of Temp Anomaly data. Will keep looking for a realllycomprehensive set.

Meanwhile the UAH data seems to be 'flat' according to one of your "Idiot" associates. I am rather a fan of areas under curves and integrals as meaningful in measuring means and trends.

I would punt that by this method there are two flatish trend lines 1979-1996, and 1998-2009 split by a sharp spike of the 97-98 ENSO. Will see if we can look at Tamas' UAH excel data match on a site somewhere.

Meanwhile we need to look forward to the debate over whether the warming is likely to 'run-away' or is nothing we can do much about.

If you subscribe to the significance of the CO2 log diff forcing as the main driver of warming in the last 25-30 years, you should have a look at this paper;

http://wattsupwiththat.com/2009/08/08/how-sensitive-is-the-earth%e2%80%99s-climate/

This guy has thought about the issues of hindcasting before forecasting - and come up with a novel proof test.

Interestingly - he has assumed lower Solar forcing content than we have seen form the raw IPCC data sets, and placed most of the correlation on the CO2 log diff formula.

The conclusions are very interesting. The difference between 'do nothing', 'do sensible' and 'do crazy' are not very much out to 2060. Pretty much what I recommend - 'do sensible' and watch.

## Kieren Diment said

at 8:48 am on Aug 14, 2009

The UAH data is not flat. It shows a positive trend. No amount of bending the truth can alter this. Wattsupwiththat has some difficulty with this as he asserts the trend since 2001 is flat, while it's just that month-to-month variability is greater than year-to-year variablity. Another decade or two of data would be required to debunk warming, and the model we've come back to here (with the consistent underestimate of temp anomaly at the end of the time series). The IPCC projections appear to take limited account of this, while Watt's projections don't. Therefore the conclusion is erroneous as it doesn't account for prediction error. QED.

## kenlambert said

at 10:35 pm on Aug 17, 2009

Attached is the UAH Excel data kindly sent to me by Tamas. The trend since 2001 is clearly cooler.

## Kieren Diment said

at 6:57 am on Aug 18, 2009

Ken,

It's not a trend, it's noise within a larger signal. You have to be particularly biased to interpret it otherwise.

The UAH data from 2001 is not a random walk either according to the PP test. But on the other hand, there is no statistically significant trend, using smothed data or otherwise, using the correct time series approach. Trying to measure a trend using unsmothed time-series data like this is dodgy anyway, as you need to correct for seasonal trends in order to ensure the "signal" is greater than the "noise". Internal seasonal trends over a short time series will mask all of the real trend without smothing.

You're clutching at straws. Better to get back to what you're good at.

## Kieren Diment said

at 6:59 am on Aug 18, 2009

I dare say you could find many instances in the unsmoothed IPCC data over the past century where the trend has appeared to have stopped for a number of years. It doesn't affect the trend as a whole. In this case, the trend has (almost certainly temporarily) stopped at the end of the time series. The correct response isn't to claim that it's stopped, it's to await the arrival of more data.

## kenlambert said

at 12:05 am on Aug 19, 2009

Well, let's wait for 10-15 years then - in the meantime do a sensible program like Ken Lambert's 10 point plan and watch what happens.

By the way you still have not explained the cyclical pattern in the Temp-CO2 residuals plot. Stubborn has pointed out that the time series variables are not iid. If that is the case, why would any of the forcing variables be iid?

## Kieren Diment said

at 7:23 am on Aug 19, 2009

Well given that the uncertainty is not as great as you claim it is, and current observations of the consequences of warming sugggest that the uncertainty is positive (i.e. the consequences of warming are more serious than we thought Tamas' delusions notwithstanding), then waiting 10-15 years would be dangerous and stupid.

The cyclical pattern in the temp-co2 residuals plot is still much smaller than the pattern of overall warming (the association between co2 and warming), so that would be just an academic exercise.

Although the forcing variable generally increase over time, their measures of central tendancy (mean, standard deviation and standard error) are meaningful. The problem with the time series specifically is that the mean and standard deviation of time is not meaningful. Having an informative mean and SD are essentially the cornerstone of these kinds of inferrential statistics.

On a side note, if you treat time as a proxy for co2 level, and thus treat time as a rank, the iid problems disappear by statistical slight of hand, although you are then answering a different question.

## Stubborn Mule said

at 8:35 am on Aug 19, 2009

Without the data, it's hard to test, but could the pattern be related to the aerosol CFC albedo effect?

## Stubborn Mule said

at 8:39 am on Aug 19, 2009

I should add, that while the individual variables may not be iid, that doesn't mean you can't go a long way with relationships between the variables. With a model along the lines of

temp = function(forcings) + residuals

you could well have a situation where neither temp nor forcings were iid, but the residuals, in which case there is a lot you can say about the statistical confidence of the model. Looking at temp ~ CO2, the residuals clearly still have a pattern there, so while a significant percentage of the variance is accounted for in the regression, there's still something there in the residuals, which is not really surprising at all (and does not undermine the thesis that CO2 is pushing temperatures up).

## Kieren Diment said

at 9:39 pm on Aug 19, 2009

And the proportion of the variance explained in the residuals is really quite small. And because we have a strong theoretical understanding of why co2 would cause the temperature to increase (the rather unassailable theory of chemical bonds), any significant co-dependent variables are likely modulated by co2. And because the residuals at the higher co2 concentrations are all negative (i.e. the model underestimates temperature), that's extremely strong evidence that the co-dependent variables are causing temperature to increase, not decrease - i.e. positive, not negative feedback.

Hence, not much point at looking at more variables in this forum, as it's a bit of an academic exercise, and while between stubborn and myself we have significant statistical (and some limited scientific) expertise, we lack the domain knowledge elsewhere.

But logical inference based on statistical theory will still get you a long way there.

## Kieren Diment said

at 9:41 pm on Aug 19, 2009

Ken,

The non random distribution of the residuals at the higher co2 concentrations (which is also the end of the time series) is very very significant from a practical point of view, and we can use this information to draw strong conclusions. The fact that they also oscillate at this point is interesting, but much less significant, due to the reasons given above.

## Stubborn Mule said

at 9:49 pm on Aug 19, 2009

Kieran: agree completely. Digging into the stats is interesting and revealing up to a certain point, but it is not done in a vacuum. It should be informed by the science as well and I would like to improve my own understanding of that science.

## Kieren Diment said

at 9:54 pm on Aug 19, 2009

Stubborn, do you agree with me about the residuals as well? (just want an explicit conformation or denial, as Ken seems to be trying to ignore that particular bit of evidence).

## kenlambert said

at 10:14 pm on Aug 19, 2009

Stubborn - here is a bit of info from the Satellite page: Might explain NH and SH Temp variations:

Ken Lambert at 11:02 pm on Aug 4, 2009

#2

With 90% of the Earth's ice in Antarctica, I would expect that the temperature response of the SH would be less linear than the NH. This is due to the roughly linear response of air and water with a constant specific heat ie. Delta F (Forcing) x Time = Delta T x Mass x Sh (specific heat constant) ....Eqan 2

ie; Delta T = Delta F x Time /Mass x Sh - a linear relationship for constant mass, time, Sh.

In the SH, ice is involved in significant quantity - it undergoes a phase change (melts) without increase in temperature – a very non-linear response........

Delta F x time = Mass x S.lat (latent heat of fusion of ice) ….Eqan 3

S.lat = 334 kJ/kG of ice. Sh water = 4.2kJ/kG-degC and Sh ice = 2.1kJ/kG-degC

Melting 1 kG of ice absorbs the same energy as raising the temperature of 1 kG of water by 79.5 degC or 1 kG of ice (below zero) by 159 degC.

So melting ice absorbs about 80 times the energy as raising the temp of water by 1 degC .

## kenlambert said

at 10:28 pm on Aug 19, 2009

AND:

"Only forcing data on aerosols I could find is from NASA/GISS (Hansen et al) Graph (b) 1850 - 2000AD”

viz; http://data.giss.nasa.gov/modelforce/trop.aer/"

#5 Don't think you understand that the Solar forcing *IS* the *variation* in INCOMING Solar Radiation which averages out at about 341 W/sq.m. (see my JUL26 and JUL28 posts).

(Remember that INCOMING Solar Radiation is TIS divided by 4 (1366/4 = 341.5 W/sq.m).)

The overall forcing balance equation for the Earth is:

(F.incoming solar at about 341W/sq.m) = (F.reflected by cloud and surface albedo at about 102 W/sq.m) + (F. outgoing longwave radiation at about 239 W/sq.m): Eqan 1

The imbalance forcings which are supposed to be heating the Earth can be taken from the above three broad terms. (Which we have postulated before ie:

Delta T (anomaly) = function (F.co2 + F.ghg + F.ozone + F.surfalbedo + F.diraerosol + F.cloudaerosol + F.solar) where these are the *VARIATIONS* in these forcing values.)

See a short explanation for the above by Kevin E. Trenberth viz:

http://www.aps.org/units/fps/newsletters/200904/trenberth.cfm

#6 kdkd "I suggest that the solar figures presented by the IPCC are solar input from the atmosphere" - this does not make sense. Go and read Trenberth and understand.

## kenlambert said

at 10:31 pm on Aug 19, 2009

Stubborn:

Tis might help your understanding of "Forcings":

The overall forcing balance equation for the Earth is:

(F.incoming solar at about 341W/sq.m) = (F.reflected by cloud and surface albedo at about 102 W/sq.m) + (F. outgoing longwave radiation at about 239 W/sq.m): Eqan 1

The imbalance forcings which are supposed to be heating the Earth can be taken from the above three broad terms. (Which we have postulated before ie:

Delta T (anomaly) = function (F.co2 + F.ghg + F.ozone + F.surfalbedo + F.diraerosol + F.cloudaerosol + F.solar) where these are the *VARIATIONS* in these forcing values.)

## kenlambert said

at 10:40 pm on Aug 19, 2009

Kieren - if you want to get a truly global set of data these are the Hadley Sea surface Temps 1850-2008.

http://hadobs.metoffice.com/hadsst2/

AND

These are the combined Land and Sea set:

http://hadobs.metoffice.com/hadcrut3/index.html

Best run these in preference to your NH set only.

## Kieren Diment said

at 10:48 pm on Aug 19, 2009

Ken, OK, you're not avoiding the karaoke. I'll grab that data and look at it as time allows. Busy reshaping the health industry to be more efficient and meet end-user's needs this week, so my time is rather limited.

## Kieren Diment said

at 10:55 pm on Aug 19, 2009

Ken, re your magical "complete model". We already know that co2 is explaining the majority of the variance in the system, and that there are extremely theoretically sound reasons for this. Therefore all other factors are of limited relevance, and given that their variation is much less sytematic, will not be driving the clear increase in the anomaly. So of course it's academically interesting, but it's highly unlikely to alter the outcome of the to-everybody-except-you-and-tamas settled debate about the role of co2 and the warming projections.

Again you're ignoring the negative residuals at the highest co2 concentrations. These are extremely important and must not be ignored, otherwise you can't understand the model properly. Positive feedback, not negative feedback. I'll try to check to see if the hadley data supports this.

## kenlambert said

at 11:01 pm on Aug 19, 2009

"Ken,

The non random distribution of the residuals at the higher co2 concentrations (which is also the end of the time series) is very very significant from a practical point of view, and we can use this information to draw strong conclusions. The fact that they also oscillate at this point is interesting, but much less significant, due to the reasons given above."

The residuals are negative cyclical Yes?

The negative could be explained by the fact that you have used only NH Temperatures with steeper trend (3.27 times steeper than the SH trend - and the non-linear ice factor.

The cyclical roughly follows the 11 year Solar cycle which is supposed to deliver approx 0.35W/sq.m (0.1% variation of 341W/sq.m incoming Solar Insolation over the surface of the Earth).

VIZ: (F.incoming solar at about 341W/sq.m) = (F.reflected by cloud and surface albedo at about 102 W/sq.m) + (F. outgoing longwave radiation at about 239 W/sq.m): Eqan 1

Any of the above three broad terms of the Earth's energy balance Eqan can have variations which will produce a net heating or cooling.

"F.outgoing" is longwave radiation is where CO2 and other GHG plays the absorbing role. We know about "F.incoming" Solar variation as above, and your modelling has not considered "F.reflected" - by aerosols (cloud ) and surface albedo.

Now tell me which of the three broad terms would have cyclical variations on an 11 year cycle? Could be all three?

## Kieren Diment said

at 11:06 pm on Aug 19, 2009

Yes, there's a fair bit of code to write to make that data into something amenable to this type of analysis, but it's doable, but it'll take me a week or so to get around to it ...

## kenlambert said

at 11:07 pm on Aug 19, 2009

If you are going to say "CO2 feedbacks" then explain why Temp goes up AND down against the steadily rising CO2 - positive feedbacks would reinforce an UP direction in Temp only - YES? (ignoring seasonal variation of course)

## Kieren Diment said

at 7:35 am on Aug 20, 2009

Ken, you're right, temperature is always variable, it has short term variation as well as the long term trend. But when we PREDICT temperature from co2 and other factors, the residual (what's left over, the error) is always negative - that is the model is consistently UNDERESTIMATING temperature at the highest co2 concentrations. So this is indeed strong evidence that "positive feedbacks would reinforce an UP direction in Temp only".

You can't eliminate the noise from any system, you have to live with it, so it's unreasonable to expect zero random error. Here we see significant random error, but we also see substantial systematic error as well, and it's the latter that allows us to draw conclusions.

## Kieren Diment said

at 7:38 am on Aug 20, 2009

So the cyclical nature of the residuals are a separate thing from them being smaller. But they still don't alter the fact that they're persistently underestimating anomaly.

I would expect this tendency to be damped in the southern hemisphere. I suppose once I can beat the hadley data into shape we can look at this, but it will take a bit of time to do.

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